Question

If a + b = s and a - b = t, then which of the following expresses the value of ab in terms of s and t?

Please help me out

Answer 1

=(s^2 - t^2)/4

Explanation:

a + b = s and a - b = t,

Add the two equations together

a + b = s

a - b = t

----------------

2a = s+t

a = (s+t)/2

Subtract the two equations

a + b = s

- a + b = -t

-------------------

2b =(s-t)

b = (s-t)/2

We want to find ab

ab = (s+t)/2 * (s-t)/2

FOIL

=(s^2 - t^2)/4